Answer
A Bhagavad Dharmi is not a devotee of any particular deity but a devotee of the Supreme Lord Himself. Therefore, he need not worry about auspicious hours, timings, constellations, or muhurtas. Deities have their special days, but the Supreme Lord has no special day — all days belong to Him, all moments belong to Him, and therefore all days and moments also belong to His devotee. For this reason, a Bhagavad Dharmi does not get caught up in such minor matters. He may get a haircut on any day. He may perform worship on any day, at any time. His entire existence is surrendered to the Lord; his every moment is worship of the Lord. Since he is a Samanvaya Yogi (one who integrates all paths), he is simultaneously a Karma Yogi, a Bhakti Yogi, a Sharanagat Yogi, and a Jnana Yogi. Prahlad was established in Sharanagat Yoga, and therefore no one could harm him. Every action of a Karma Yogi is offered to the Lord, and that offering itself becomes his worship. Whenever any action is surrendered to the Lord, that action transcends the constraints of auspicious hours and muhurtas. When the Lord Himself has accepted his action, what planet or constellation can possibly cause him harm? A Bhagavad Dharmi does not worry about these minor matters. Reflect upon these verses of the Gita — 'Shubhashubhaphalairevam mokshyase karmabandhanaihi | Sannyasayogayuktatma vimukto mamupaisyasi' (9:28). Meaning: In this way, one whose every action is an offering to Me, the Lord, who has renounced attachment to the fruits of action — such a person, whose mind is united with this yoga of renunciation, shall be freed from the bondage of karma that bears auspicious and inauspicious results, and having been thus liberated, shall attain Me alone.
'Yo na hrishyati na dveshti na shochati na kankshati' — Meaning: One who neither rejoices nor hates, who neither grieves nor desires, who has renounced both the auspicious and the inauspicious — such a devotee is dear to Me!
The purport of these two verses I have cited from the Gita is that a person's actions rise above the categories of auspicious and inauspicious when they are surrendered to the Lord, or when attachment to their fruits is destroyed. Therefore, if you perform your haircut or any other activity as an offering to the Lord, it is not necessary to look for auspicious hours, muhurtas, or days. The prescriptions of auspicious hours, muhurtas, and days are meant for ordinary individuals.